Resonant integrated optical gyroscopes (RIOGs) can integrate discrete optical components as a promising candidate for high-performance micro-optical gyroscopes. However, the current RIOG still consists of discrete elements due to the difficulty and complexity of heterogeneous integration of resonator and modulators. This paper presents on-chip integration of optical functional components including modulator, resonator, beam splitter, and coupler for the organic-polymer-based RIOG. Simple integrated optical processes such as spin coating, lithography, and etching can realize RIOG chips with low cost, size, weight, and power (CSWaP) features. Thereinto, the electro-optic modulator (EOM) fabricated by self-synthesized electro-optic (EO) polymer (side chain bonded polyurethane imide) exhibits less than 2 V half-wave voltage, which is half of the lithium niobate (LiNbO3) modulator. With respect to the resonator, a quality factor of approximately million was achieved using low-loss fluorinated polymer. In addition, the angular velocity sensing of RIOG was also investigated. By demonstrating the monolithic integration of the resonator and modulators, such an all-polymer RIOG chip prototype builds the technical foundation for the precision fully integrated optical gyroscope.